A non-relativistic classification of charged molecular hydrogenic, helium andmixed helium-hydrogenic chains with one or two electrons which can exist in astrong magnetic field $B \lesssim 10^{16} $G is given. It is shown that forboth $1e-2e$ cases at the strongest studied magnetic fields the longesthydrogenic chain contains at most five protons indicating to the existence ofthe $\rm{H}_5^{4+}$ and $\rm{H}_5^{3+}$ ions, respectively. In the case of thehelium chains the longest chains can exist at the strongest studied magneticfields with three and four $\al-$particles for $1e-2e$ cases, respectively. Formixed helium-hydrogenic chains the number of heavy centers can reach five forhighest magnetic fields studied. In general, for a fixed magnetic fieldtwo-electron chains are more bound than one-electron ones.
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